http://www.users.qwest.net/~rnclark
How fine should sampling be to record all the detail? There is the well known Nyquist theorem that says if you sample 2 samples per cycle you get all the information possible. This theorem assumes the sampling is in phase with the signal, meaning one samples at the highs and lows of a sinusoidal signal. Image sampling is not in phase with the image detail.
To illustrate the effect and to show how much sampling is needed, a 100 lines/inch (3.94 lines/mm) Ronchi rulling was scanned in transmittance on a scanner that had 2400 dpi optical resolution. The rulling was tilted slightly so that the phase between scanner pixels and lines on the rulling varied in position along the scan. Scans were done at different dpi to illustrate sampling effects. Results are below.
The results illustrate sampling errors occur at sampling less than 6x the lines/length (3x Nyquist). Note the black/white phase inversion in some of the samples, like 100 dpi (0.5x Nyquist) and Nyquist sampling (200 dpi). Only the 3x Nyquist shows a clean pattern free of artifacts. (Not shown: the 2x Nyquist shows patterns similar to 1.5x sampling, just with horizontal banding closer together).
The illustrations here apply to sampling out of phase signals in general, whether it is a scanner scanning film detail, or a digital camera recording image detail.
Now let's look at a real example. This is the same
image used in the
scan and
image detail web page.
In real images, image detail is often limited
by diffraction, lens aberrations, the detector, or
other things, like blur or motion. The image below is limited
mainly by diffraction and some by film grain.
How much sampling does one need in a near diffraction-limited
image?
The 3300 dpi scan (top image) is 7.7-micron pixels, or about 3 pixels per cycle at the Dawes limit. The next image is 2 pixels per cycle at the at the Rayleigh limit. There is slight degradation of the image. Sampling less than this rapidly lowers image detail as seen in the bottom two images. The conclusion is 2 to 3 pixels per cycle at the Dawes limit records close to all the detail in the image, but 2 pixels per cycle at the Rayleigh limit is pretty close.
Image detail and other scanning and
digital info.
Photography Home Page.
Landscape Photo Gallery Index.
Nature Photos Gallery Index.
Astro Photos
R. N. Clark
rnclark@qwest.net
Last updated Oct. 31, 2001.